Trailer length and hitch angle bias estimation

ABSTRACT

A backup assist system for a vehicle and trailer combination includes a steering system and a first sensor detecting a first dynamic condition of the combination. The system further includes a controller receiving a value for the first dynamic condition from the first sensor at a plurality of instances. The controller further solves for a corresponding plurality of parameters in a kinematic model of the combination and controls the steering system using the plurality of parameters in the kinematic model.

FIELD OF THE INVENTION

The disclosure made herein relates generally to trailer motion andparameter estimation, and more particularly to a length estimation for atrailer using yaw signals in a system to assist with vehicle guidance ofthe trailer, such as a trailer backup assist system.

BACKGROUND OF THE INVENTION

Reversing a vehicle while towing a trailer can be challenging for manydrivers, particularly for drivers that drive with a trailer on aninfrequent basis or with various types of trailers. Systems used toassist a driver with backing a trailer frequently estimate the positionof the trailer relative to the vehicle with a sensor or the like thatdetermines a steering input for the vehicle based on an input trailercurvature path and determined a hitch angle. Both the hitch angledetermination and the steering input determination require use of akinematic model of the combined trailer and vehicle that includes thelength of the trailer, more particularly, from the point of attachmentwith the vehicle to center of the axles thereof. While some systems haverelied on user input for the trailer length, doing so may place anundesired burden on the user and may introduce inaccuracies that somesuch systems are unequipped to handle. The accuracy and reliability ofthe calculations involving trailer length can be critical to theoperation of the backup assist system. Accordingly, improvements relatedto automated system estimation of trailer length in an accurate mannermay be desired.

SUMMARY OF THE INVENTION

According to one aspect of the present invention, a backup assist systemfor a vehicle and trailer combination includes a steering system and afirst sensor detecting a first dynamic condition of the combination. Thesystem further includes a controller receiving a value for the firstdynamic condition from the first sensor at a plurality of instances. Thecontroller further solves for a corresponding plurality of parameters ina kinematic model of the combination and controls the steering systemusing the plurality of parameters in the kinematic model.

According to another aspect of the present invention, a vehicle includesa steering system, a first sensor detecting a first dynamic condition ofat least one of the vehicle or the vehicle in a combination with atrailer, and a trailer backup assist system. The trailer backup assistsystem includes a controller receiving a value for the first dynamiccondition from the first sensor at a plurality of instances, solving fora corresponding plurality of parameters in a kinematic model of thecombination, and controlling the steering system using the plurality ofparameters in the kinematic model.

According to another aspect of the present invention, a method forassisting a vehicle in reversing a trailer includes determining unknownvalues for a plurality of parameters in a combination of the vehicle andthe trailer, which includes receiving a measurement for a first dynamiccondition of the combination at a plurality of instances and solving forthe parameters in a kinematic model of the combination. The methodfurther includes implementing a reversing operation includingcontrolling a vehicle steering system using the plurality of parameters.

These and other aspects, objects, and features of the present inventionwill be understood and appreciated by those skilled in the art uponstudying the following specification, claims, and appended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIG. 1 is a top perspective view of a vehicle attached to a trailer withone embodiment of a hitch angle sensor for operating a trailer backupassist system;

FIG. 2 is a block diagram illustrating one embodiment of the trailerbackup assist system having a steering input device, a curvaturecontroller, and a trailer braking system;

FIG. 3 is a schematic diagram that illustrates the geometry of a vehicleand a trailer overlaid with a two-dimensional x-y coordinate system,identifying variables used to determine a kinematic relationship of thevehicle and the trailer for the trailer backup assist system, accordingto one embodiment;

FIG. 4 is a flowchart depicting a process for determining one or moreunknown variables of the kinematic relationship that can be implementedby the trailer backup assist system;

FIG. 5 is a flowchart depicting a variation of the process of FIG. 4 fordetermining a trailer length and a hitch angle offset;

FIG. 6 is a flowchart depicting a variation of the process of FIG. 4 fordetermining a trailer length, a hitch angle offset, and a drawbarlength;

FIG. 7 is a flowchart depicting an alternative variation of the processof FIG. 4 for determining a trailer length and a hitch angle offset;

FIG. 8 is a flowchart depicting an alternative process for determiningone or more unknown variables of the kinematic relationship that can beimplemented by the trailer backup assist system;

FIGS. 9 and 10 are graphs showing a linear curves fit to data setsobtained from vehicle and trailer sensors relating a hitch angle to asteering angle of a vehicle;

FIG. 11 is a graph depicting a relationship between the slope of alinear curve fit to data relating a hitch angle to a steering angle of avehicle and increasing trailer length;

FIG. 12 is a schematic depiction of a control scheme for steering atrailer along a backing path;

FIG. 13 diagram showing a relationship between a hitch angle and asteering angle of the vehicle as it relates to curvature of the trailerand a jackknife angle;

FIG. 14 is a plan view of a steering input device having a rotatableknob for operating the trailer backup assist system, according to oneembodiment;

FIG. 15 is a plan view of another embodiment of a rotatable knob forselecting a desired curvature of a trailer and a corresponding schematicdiagram illustrating a vehicle and a trailer with various trailercurvature paths correlating with desired curvatures that may beselected;

FIG. 16 is a schematic diagram showing a backup sequence of a vehicleand a trailer implementing various curvature selections with the trailerbackup assist system, according to one embodiment; and

FIG. 17 is a flow diagram illustrating a method of operating a trailerbackup assist system using an operating routine for steering a vehiclereversing a trailer with normalized control of the desired curvature,according to one embodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

For purposes of description herein, the terms “upper,” “lower,” “right,”“left,” “rear,” “front,” “vertical,” “horizontal,” “interior,”“exterior,” and derivatives thereof shall relate to the invention asoriented in FIG. 1. However, it is to be understood that the inventionmay assume various alternative orientations, except where expresslyspecified to the contrary. It is also to be understood that the specificdevices and processes illustrated in the attached drawing, and describedin the following specification are simply exemplary embodiments of theinventive concepts defined in the appended claims. Hence, specificdimensions and other physical characteristics relating to theembodiments disclosed herein are not to be considered as limiting,unless the claims expressly state otherwise. Additionally, unlessotherwise specified, it is to be understood that discussion of aparticular feature of component extending in or along a given directionor the like does not mean that the feature or component follows astraight line or axis in such a direction or that it only extends insuch direction or on such a plane without other directional componentsor deviations, unless otherwise specified.

Referring to FIGS. 1-3, reference numeral 10 generally designates atrailer backup assist system for controlling a backing path of a trailer12 attached to a vehicle 14 by allowing a driver of the vehicle 14 tospecify a desired curvature 26 of the backing path of the trailer 12. Inone embodiment, the trailer backup assist system 10 automatically steersthe vehicle 14 to guide the trailer 12 on the desired curvature orbacking path 26 as a driver uses the accelerator and brake pedals tocontrol the reversing speed of the vehicle 14. To monitor the positionof the trailer 12 relative to the vehicle 14, the trailer backup assistsystem 10 may include a sensor system 16 that senses or otherwisedetermines a hitch angle γ between the trailer 12 and the vehicle 14. Inone embodiment, the sensor system 16 may include a hitch angle sensor44. In some implementations, the hitch angle sensor 44 may exhibit abias in the reading that results in the measured hitch angle γ_(m) beingoffset from the actual hitch angle γ by an offset angle γ_(o).Additionally, as explained further below, backup assist system 10 mayrequire various other parameters relating to the geometry of thecombined trailer 12 and vehicle 14 to implement a routine that controlsthe backing of trailer 12. In an embodiment, backup assist system 10includes a steering system 62 and a first sensor detecting a firstdynamic condition of the combination. The system 10 further includes acontroller 28 receiving a value for the first dynamic condition from thefirst sensor at a plurality of instances. The controller 28 furthersolves for a corresponding plurality of parameters in a kinematic modelof the combination and controls the steering system 62 using theplurality of parameters in the kinematic model.

With respect to the general operation of the trailer backup assistsystem 10, a steering input device 18 may be provided, such as arotatable knob 30, for a driver to provide the desired curvature 26 ofthe trailer 12. As such, the steering input device 18 may be operablebetween a plurality of selections, such as successive rotated positionsof a knob 30, that each provide an incremental change to the desiredcurvature 26 of the trailer 12. Upon inputting the desired curvature 26,the controller may generate a steering command for the vehicle 14 toguide the trailer 12 on the desired curvature 26 based on the estimatedhitch angle γ and a kinematic relationship between the trailer 12 andthe vehicle 14. In other embodiments, the hitch angle γ may becontrolled using knob 30 such that the system 10 derives a steeringcommand to achieve and maintain such a hitch angle γ. Therefore, theaccuracy of the hitch angle estimation, and accordingly, the trailerlength estimation is significant in operating the trailer backup assistsystem 10.

With reference to the embodiment shown in FIG. 1, the vehicle 14 is apickup truck embodiment that is equipped with one embodiment of thetrailer backup assist system 10 for controlling the backing path of thetrailer 12 that is attached to the vehicle 14. Specifically, the vehicle14 is pivotally attached to one embodiment of the trailer 12 that has abox frame 32 with an enclosed cargo area 34, a single axle having aright wheel assembly and a left wheel assembly, and a tongue 36longitudinally extending forward from the enclosed cargo area 34. Theillustrated trailer 12 also has a trailer hitch connector in the form ofa coupler assembly 38 that is connected to a vehicle hitch connector inthe form of a hitch ball 40. The coupler assembly 38 latches onto thehitch ball 40 to provide a pivoting ball joint connection 42 that allowsfor articulation of the hitch angle γ. It should be appreciated thatadditional embodiments of the trailer 12 may alternatively couple withthe vehicle 14 to provide a pivoting connection, such as by connectingwith a fifth wheel connector. It is also contemplated that additionalembodiments of the trailer may include more than one axle and may havevarious shapes and sizes configured for different loads and items, suchas a boat trailer or a flatbed trailer.

Still referring to FIG. 1, the sensor system 16 in the illustratedembodiment includes a sensor module 20 that may include a housed sensorcluster 21 mounted on the tongue 36 of the trailer 12 proximate theenclosed cargo area 34 and includes left and right wheel speed sensors23 on laterally opposing wheels of the trailer 12. It is conceivablethat the wheel speed sensors 23 may be bi-directional wheel speedsensors for monitoring both forward and reverse speeds. Also, it iscontemplated that the sensor cluster 21 in additional embodiments may bemounted on alternative portions of the trailer 12. The sensor module 20generates a plurality of signals indicative of various dynamics of thetrailer 12. The signals may include a yaw rate signal, a lateralacceleration signal, and wheel speed signals generated respectively by ayaw rate sensor 25, an accelerometer 27, and the wheel speed sensors 23.

In the illustrated embodiment, the yaw rate sensor 25 and theaccelerometer 27 are contained within the housed sensor cluster 21,although other configurations are conceivable. It is conceivable thatthe accelerometer 27, in some embodiments, may be two or more separatesensors and may be arranged at an offset angle, such as two sensorsarranged at plus and minus forty-five degrees from the longitudinaldirection of the trailer or arranged parallel with the longitudinal andlateral directions of the trailer, to generate a more robustacceleration signal. It is also contemplated that these sensor signalscould be compensated and filtered to remove offsets or drifts, andsmooth out noise. Further, the controller 28 may utilizes processedsignals received outside of the sensor system 16, including standardsignals from the brake control system 72 and the power assist steeringsystem 62, such as vehicle yaw rate ω₁, vehicle speed v₁, and steeringangle δ, to estimate, by various calculations, unknown parameters thatfit within a kinematic model of the vehicle-trailer combination, asillustrated in FIG. 3. Such parameters may include the trailer hitchangle γ, trailer speed and related trailer parameters, such as thetrailer length D, or the trailer hitch length L. As described in moredetail below, the controller 28 may estimate the hitch angle γ, or mayestimate an offset between a measured hitch angle γ_(m) (such as by ahitch angle sensor) and an actual hitch angle γ based on various otherknown parameters in view of the kinematic model of the relationshipbetween the trailer 12 and the vehicle 14. The controller 28 of thetrailer backup assist system 10 may also utilize the estimated variablesand parameters to control the steering system 62, brake control system72, and the powertrain control system 74, such as to assist backing thevehicle-trailer combination or to mitigate a trailer sway conditionaccording to further calculations based on the kinematic model.

The sensor system 16 may also a vision-based hitch angle sensor 44 formeasuring the hitch angle γ between the vehicle 14 and the trailer 12.In an embodiment wherein the hitch angle γ is determined using othermeasured parameters in view of the kinematic relationship between thetrailer 12 and the vehicle 14, the vision-based hitch angle sensor 44may be used as a backup system or as an additional check on the valueobtained using the kinematic model. In other embodiments, the trailerangle γ may not be estimated or calculated directly using the kinematicmodel, the system 10 instead calculating an offset γ_(o) between ameasured hitch angle γ_(m) and the actual hitch angle γ such that theoffset γ_(o) can be added to subsequent measured hitch angles γ_(m) tocompensate for such an offset in continuing to use the vision-basedhitch angle sensor 44 to obtain values for the hitch angle γ. In anotherembodiment, the vision-based hitch angle sensor 44 may be omittedentirely with an estimate of hitch angle γ being calculated using knownor measured parameters in the kinematic model.

When present, the illustrated hitch angle sensor 44 employs a camera 46(e.g. video imaging camera) that may be located proximate an upperregion of the vehicle tailgate 48 at the rear of the vehicle 14, asshown, such that the camera 46 may be elevated relative to the tongue 36of the trailer 12. The illustrated camera 46 has an imaging field ofview 50 located and oriented to capture one or more images of thetrailer 12, including a region containing one or more desired targetplacement zones for at least one target 52 to be secured. Although it iscontemplated that the camera 46 may capture images of the trailer 12without a target 52 to determine the hitch angle γ, in the illustratedembodiment, the trailer backup assist system 10 includes a target 52placed on the trailer 12 to allow the trailer backup assist system 10 toutilize information acquired via image acquisition and processing of thetarget 52. For instance, the illustrated camera 46 may include a videoimaging camera that repeatedly captures successive images of the trailer12 that may be processed to identify the target 52 and its location onthe trailer 12 for determining movement of the target 52 and the trailer12 relative to the vehicle 14 and the corresponding hitch angle γ. Itshould also be appreciated that the camera 46 may include one or morevideo imaging cameras and may be located at other locations on thevehicle 14 to acquire images of the trailer 12 and the desired targetplacement zone, such as on a passenger cab 54 of the vehicle 14 tocapture images of a gooseneck trailer. Furthermore, it is contemplatedthat additional embodiments of the hitch angle sensor 44 and the sensorsystem 16 for providing the hitch angle γ may include one or acombination of a potentiometer, a magnetic-based sensor, an opticalsensor, a proximity sensor, a rotational sensor, a capacitive sensor, aninductive sensor, or a mechanical based sensor, such as a mechanicalsensor assembly mounted to the pivoting ball joint connection 42, energytransducers of a reverse aid system, a blind spot system, and/or a crosstraffic alert system, and other conceivable sensors or indicators of thehitch angle γ to supplement or be used in place of the vision-basedhitch angle sensor 44.

With reference to the embodiment of the trailer backup assist system 10shown in FIG. 2, the hitch angle sensor 44 is provided in dashed linesto illustrate that in some embodiments it may be omitted, such as whenthe trailer sensor module 20 is provided and used to estimate hitchangle γ. The illustrated embodiment of the trailer backup assist system10 receives vehicle and trailer status-related information fromadditional sensors and devices. This information includes positioninginformation from a positioning device 56, which may include a globalpositioning system (GPS) on the vehicle 14 or a handled device, todetermine a coordinate location of the vehicle 14 and the trailer 12based on the location of the positioning device 56 with respect to thetrailer 12 and/or the vehicle 14 and based on the estimated hitch angleγ. The positioning device 56 may additionally or alternatively include adead reckoning system for determining the coordinate location of thevehicle 14 and the trailer 12 within a localized coordinate system basedat least on vehicle speed, steering angle, and hitch angle γ. Othervehicle information received by the trailer backup assist system 10 mayinclude a speed of the vehicle 14 from a speed sensor 58 and a yaw rateof the vehicle 14 from a yaw rate sensor 60. It is contemplated that inadditional embodiments, the hitch angle sensor 44 and other vehiclesensors and devices may provide sensor signals or other information,such as proximity sensor signals or successive images of the trailer 12,that the controller of the trailer backup assist system 10 may processwith various routines to determine an indicator of the hitch angle γ,such as a range of hitch angles.

As further shown in FIG. 2, one embodiment of the trailer backup assistsystem 10 is in communication with a power assist steering system 62 ofthe vehicle 14 to operate the steered wheels 64 (FIG. 1) of the vehicle14 for moving the vehicle 14 in such a manner that the trailer 12 reactsin accordance with the desired curvature 26 of the trailer 12. In theillustrated embodiment, the power assist steering system 62 is anelectric power-assisted steering (EPAS) system that includes an electricsteering motor 66 for turning the steered wheels 64 to a steering anglebased on a steering command, whereby the steering angle may be sensed bya steering angle sensor 67 of the power assist steering system 62. Thesteering command may be provided by the trailer backup assist system 10for autonomously steering during a backup maneuver and may alternativelybe provided manually via a rotational position (e.g., steering wheelangle) of a steering wheel 68 (FIG. 1). However, in the illustratedembodiment, the steering wheel 68 of the vehicle 14 is mechanicallycoupled with the steered wheels 64 of the vehicle 14, such that thesteering wheel 68 moves in concert with steered wheels 64, preventingmanual intervention with the steering wheel 68 during autonomoussteering. More specifically, a torque sensor 70 is provided on the powerassist steering system 62 that senses torque on the steering wheel 68that is not expected from autonomous control of the steering wheel 68and therefore indicative of manual intervention, whereby the trailerbackup assist system 10 may alert the driver to discontinue manualintervention with the steering wheel 68 and/or discontinue autonomoussteering.

In alternative embodiments, some vehicles have a power assist steeringsystem 62 that allows a steering wheel 68 to be partially decoupled frommovement of the steered wheels 64 of such a vehicle. Accordingly, thesteering wheel 68 can be rotated independent of the manner in which thepower assist steering system 62 of the vehicle controls the steeredwheels 64 (e.g., autonomous steering as commanded by the trailer backupassist system 10). As such, in these types of vehicles where thesteering wheel 68 can be selectively decoupled from the steered wheels64 to allow independent operation thereof, the steering wheel 68 may beused as a steering input device 18 for the trailer backup assist system10, as disclosed in greater detail herein.

Referring again to the embodiment illustrated in FIG. 2, the powerassist steering system 62 provides the controller 28 of the trailerbackup assist system 10 with information relating to a rotationalposition of steered wheels 64 of the vehicle 14, including a steeringangle. The controller 28 in the illustrated embodiment processes thecurrent steering angle δ, in addition to other vehicle 14 and trailer 12conditions to guide the trailer 12 along the desired curvature 26. It isconceivable that the trailer backup assist system 10, in additionalembodiments, may be an integrated component of the power assist steeringsystem 62. For example, the power assist steering system 62 may includea trailer backup assist algorithm for generating vehicle steeringinformation and commands as a function of all or a portion ofinformation received from the steering input device 18, the hitch anglesensor 44, the power assist steering system 62, a vehicle brake controlsystem 72, a powertrain control system 74, and other vehicle sensors anddevices.

As also illustrated in FIG. 2, the vehicle brake control system 72 mayalso communicate with the controller 28 to provide the trailer backupassist system 10 with braking information, such as vehicle wheel speed,and to receive braking commands from the controller 28. For instance,vehicle speed information can be determined from individual wheel speedsas monitored by the brake control system 72. Vehicle speed may also bedetermined from the powertrain control system 74, the speed sensor 58,and the positioning device 56, among other conceivable means. In someembodiments, individual wheel speeds can also be used to determine avehicle yaw rate, which can be provided to the trailer backup assistsystem 10 in the alternative or in addition to the vehicle yaw ratesensor 60. In certain embodiments, the trailer backup assist system 10can provide vehicle braking information to the brake control system 72for allowing the trailer backup assist system 10 to control braking ofthe vehicle 14 during backing of the trailer 12. For example, thetrailer backup assist system 10 in some embodiments may regulate speedof the vehicle 14 during backing of the trailer 12, which can reduce thepotential for unacceptable trailer backup conditions. Examples ofunacceptable trailer backup conditions include, but are not limited to,a vehicle 14 over speed condition, a high hitch angle rate, trailerangle dynamic instability, a calculated theoretical trailer jackknifecondition (defined by a maximum vehicle steering angle, drawbar length,tow vehicle wheelbase, and an effective trailer length), or physicalcontact jackknife limitation (defined by an angular displacement limitrelative to the vehicle 14 and the trailer 12), and the like. It isdisclosed herein that the trailer backup assist system 10 can issue analert signal corresponding to a notification of an actual, impending,and/or anticipated unacceptable trailer backup condition.

The powertrain control system 74, as shown in the embodiment illustratedin FIG. 2, may also interact with the trailer backup assist system 10for regulating speed and acceleration of the vehicle 14 during backingof the trailer 12. As mentioned above, regulation of the speed of thevehicle 14 may be necessary to limit the potential for unacceptabletrailer backup conditions such as, for example, jackknifing and trailerangle dynamic instability. Similar to high-speed considerations as theyrelate to unacceptable trailer backup conditions, high acceleration andhigh dynamic driver curvature requests can also lead to suchunacceptable trailer backup conditions.

With continued reference to FIG. 2, the trailer backup assist system 10in the illustrated embodiment may communicate with one or more devices,including a vehicle alert system 76, which may prompt visual, auditory,and tactile warnings. For instance, vehicle brake lights 78 and vehicleemergency flashers may provide a visual alert and a vehicle horn 79and/or speaker 81 may provide an audible alert. Additionally, thetrailer backup assist system 10 and/or vehicle alert system 76 maycommunicate with a human machine interface (HMI) 80 for the vehicle 14.The HMI 80 may include a vehicle display 82, such as a center-stackmounted navigation or entertainment display (FIG. 1). Further, thetrailer backup assist system 10 may communicate via wirelesscommunication with another embodiment of the HMI 80, such as with one ormore handheld or portable devices, including one or more smartphones.The portable device may also include the display 82 for displaying oneor more images and other information to a user. For instance, theportable device may display one or more images of the trailer 12 and anindication of the estimated hitch angle on the display 82. In addition,the portable device may provide feedback information, such as visual,audible, and tactile alerts.

As further illustrated in FIG. 2, the trailer backup assist system 10includes a steering input device 18 that is connected to the controller28 for allowing communication of information therebetween. It isdisclosed herein that the steering input device 18 can be coupled to thecontroller 28 in a wired or wireless manner. The steering input device18 provides the trailer backup assist system 10 with informationdefining the desired backing path of travel of the trailer 12 for thecontroller 28 to process and generate steering commands. Morespecifically, the steering input device 18 may provide a selection orpositional information that correlates with a desired curvature 26 ofthe desired backing path of travel of the trailer 12. Also, the trailersteering commands provided by the steering input device 18 can includeinformation relating to a commanded change in the path of travel, suchas an incremental change in the desired curvature 26, and informationrelating to an indication that the trailer 12 is to travel along a pathdefined by a longitudinal centerline axis of the trailer 12, such as adesired curvature value of zero that defines a substantially straightpath of travel for the trailer. As will be discussed below in moredetail, the steering input device 18 according to one embodiment mayinclude a movable control input device for allowing a driver of thevehicle 14 to command desired trailer steering actions or otherwiseselect and alter a desired curvature. For instance, the moveable controlinput device may be a rotatable knob 30 (see FIGS. 14 and 15), which canbe rotatable about a rotational axis extending through a top surface orface of the knob 30. In other embodiments, the rotatable knob 30 may berotatable about a rotational axis extending substantially parallel to atop surface or face of the rotatable knob 30. Furthermore, the steeringinput device 18, according to additional embodiments, may includealternative devices for providing a desired curvature 26 or otherinformation defining a desired backing path, such as a joystick, akeypad, a series of depressible buttons or switches, a sliding inputdevice, various user interfaces on a touch-screen display, a visionbased system for receiving gestures, a control interface on a portabledevice, and other conceivable input devices as generally understood byone having ordinary skill in the art. It is contemplated that thesteering input device 18 may also function as an input device for otherfeatures, such as providing inputs for other vehicle features orsystems.

Still referring to the embodiment shown in FIG. 2, the controller 28 isconfigured with a microprocessor 84 to process logic and routines storedin memory 86 that receive information from the sensor system 16,including the trailer sensor module 20, the hitch angle sensor 44, thesteering input device 18, the power assist steering system 62, thevehicle brake control system 72, the trailer braking system, thepowertrain control system 74, and other vehicle sensors and devices. Thecontroller 28 may generate vehicle steering information and commands asa function of all or a portion of the information received. Thereafter,the vehicle steering information and commands may be provided to thepower assist steering system 62 for affecting steering of the vehicle 14to achieve a commanded path of travel for the trailer 12. The controller28 may include the microprocessor 84 and/or other analog and/or digitalcircuitry for processing one or more routines. Also, the controller 28may include the memory 86 for storing one or more routines, including ahitch angle estimation routine 130, an operating routine 132, and acurvature routine 98. It should be appreciated that the controller 28may be a stand-alone dedicated controller or may be a shared controllerintegrated with other control functions, such as integrated with thesensor system 16, the power assist steering system 62, and otherconceivable onboard or off-board vehicle control systems.

With reference to FIG. 3, we now turn to a discussion of vehicle andtrailer information and parameters used to calculate a kinematicrelationship between a curvature of a path of travel of the trailer 12and the steering angle of the vehicle 14 towing the trailer 12, whichcan be desirable for a trailer backup assist system 10 configured inaccordance with some embodiments, including for use by a curvatureroutine 98 of the controller 28 in one embodiment. To achieve such akinematic relationship, certain assumptions may be made with regard toparameters associated with the vehicle/trailer system. Examples of suchassumptions include, but are not limited to, the trailer 12 being backedby the vehicle 14 at a relatively low speed, wheels of the vehicle 14and the trailer 12 having negligible (e.g., no) slip, tires of thevehicle 14 having negligible (e.g., no) lateral compliance, tires of thevehicle 14 and the trailer 12 having negligible (e.g., no) deformation,actuator dynamics of the vehicle 14 being negligible, and the vehicle 14and the trailer 12 exhibiting negligible (e.g., no) roll or pitchmotions, among other conceivable factors with the potential to have aneffect on controlling the trailer 12 with the vehicle 14.

As shown in FIG. 3, for a system defined by a vehicle 14 and a trailer12, the kinematic relationship is based on various parameters associatedwith the vehicle 14 and the trailer 12. These parameters include:

δ: steering angle at steered front wheels of the vehicle;

α: yaw angle of the vehicle;

β: yaw angle of the trailer;

γ: hitch angle (γ=β−α);

W: wheel base of the vehicle;

L: drawbar length between hitch point and rear axle of the vehicle;

D: distance (trailer length) between hitch point and axle of the traileror effective axle for a multiple axle trailer; and

r₂: curvature radius for the trailer.

One embodiment of a kinematic relationship between trailer path radiusof curvature r₂ at the midpoint of an axle of the trailer 12, steeringangle δ of the steered wheels 64 of the vehicle 14, and the hitch angleγ can be expressed in the equation provided below. As such, if the hitchangle γ is provided, the trailer path curvature κ₂ can be controlledbased on regulating the steering angle δ (where {dot over (β)} istrailer yaw rate and {dot over (η)} is trailer velocity).

$\kappa_{2} = {\frac{1}{r_{2}} = {\frac{\overset{.}{\beta}}{\overset{.}{\eta}} = \frac{{\left( {W + \frac{{KV}^{2}}{g}} \right)\sin\;\gamma} + {L\;\cos\;\gamma\;\tan\;\delta}}{\left( {{\left( {W + \frac{{KV}^{2}}{g}} \right)\cos\;\gamma} - {L\;\sin\;\gamma\;\tan\;\delta}} \right)}}}$

This relationship can be expressed to provide the steering angle δ as afunction of trailer path curvature κ₂ and hitch angle γ.

$\delta = {{\tan^{- 1}\left( \frac{\left( {W + \frac{{KV}^{2}}{g}} \right)\left\lbrack {{\kappa_{2}D\;\cos\;\gamma} - {\sin\;\gamma}} \right\rbrack}{{{DL}\;\kappa_{2}\sin\;\gamma} + {L\;\cos\;\gamma}} \right)} = {F\left( {\gamma,\kappa_{2},K} \right)}}$

Accordingly, for a particular vehicle and trailer combination, certainparameters (e.g., D, W and L) of the kinematic relationship are constantand assumed known when completing a backup operating involvingoutputting steering angle δ. V is the vehicle longitudinal speed and gis the acceleration due to gravity. K is a speed dependent parameterwhich when set to zero makes the calculation of steering angleindependent of vehicle speed. For example, vehicle-specific parametersof the kinematic relationship can be predefined in an electronic controlsystem of the vehicle 14 and trailer-specific parameters of thekinematic relationship can be inputted by a driver of the vehicle 14,determined from sensed trailer behavior in response to vehicle steeringcommands, or otherwise determined from signals provided by the trailer12. Trailer path curvature κ₂ can be determined from the driver inputvia the steering input device 18. Through the use of the equation forproviding steering angle, a corresponding steering command can begenerated by the curvature routine 98 for controlling the power assiststeering system 62 of the vehicle 14.

In an additional embodiment, an assumption may be made by the curvatureroutine 98 that a longitudinal distance L between the pivotingconnection and the rear axle of the vehicle 14 is equal to zero forpurposes of operating the trailer backup assist system 10 when agooseneck trailer or other similar trailer is connected with the a hitchball or a fifth wheel connector located over a rear axle of the vehicle14. The assumption essentially assumes that the pivoting connection withthe trailer 12 is substantially vertically aligned with the rear axle ofthe vehicle 14. When such an assumption is made, the controller 28 maygenerate the steering angle command for the vehicle 14 as a functionindependent of the longitudinal distance L between the pivotingconnection and the rear axle of the vehicle 14. It is appreciated thatthe gooseneck trailer mentioned generally refers to the tongueconfiguration being elevated to attach with the vehicle 14 at anelevated location over the rear axle, such as within a bed of a truck,whereby embodiments of the gooseneck trailer may include flatbed cargoareas, enclosed cargo areas, campers, cattle trailers, horse trailers,lowboy trailers, and other conceivable trailers with such a tongueconfiguration.

As can be appreciated based on the foregoing, there are various ones ofthe kinematic parameters in the curvature κ₂ and steering input δequations that are generally fixed and correspond to the dimensions ofthe vehicle 14 and trailer 12 combination. Specifically, the length D ofthe trailer 12, the wheel base W of the vehicle 14, and the distance Lfrom the hitch connection H to the rear axle of the vehicle 14 aregenerally fixed and may be stored in the memory 86 of system 10 (FIG.2), whereas other kinematic parameters may be dynamic and obtained fromtrailer sensor module 20 and vehicle sensors 17 on an ongoing basis. Itis noted that the wheel base of the vehicle 14 and the distance from thehitch connection to the rear axle of the vehicle 14 relate only tovehicle 14 itself, within which the controller 28 and, accordingly,memory 86 are installed. It follows, then, these parameters may bestored in memory 86 during manufacture of vehicle 14, or duringinstallation of the relevant portions of system 10 therein, as they areknown in relation to the specific make and model of the particularvehicle 14. On the other hand, the length D of the trailer 12, whilefixed with respect to a particular initiated operating routine 132, mayvary as different trailers 12 are hitched to vehicle 14 for towingthereby. Further, the particular trailer 12 with which a given vehicle14 will be used may not be known during manufacture of vehicle 14 orinstallation of system 10, and a user of such a vehicle 14 may wish touse vehicle 14 in various operating routines 132 with various trailers12 of different sizes and configurations. Accordingly, a routine forsystem 10 obtaining the particular trailer length D of a trailer hitchedwith vehicle 14 may be needed and may be required prior to system 10implementing operating routine 132. In further aspects, various trailerhitch assemblies may be used with vehicle 14 such that the particularvalue for L may also vary. Accordingly, the estimation routine 130 forsystem 10 obtaining the trailer length D may also obtain drawbar lengthL prior to operation of curvature routine 98.

Turning now to FIG. 4, in various embodiments, controller 28 candetermine one or more unknown values or parameters of the kinematicmodel using a series of inputs regarding known or measurable values. Invarious examples described herein, this can be done by taking inputsregarding measurable dynamic parameters of the kinematic model at anumber of intervals that correspond to the number of unknown values suchthat various equations derived from the kinematic model can be solvedfor the unknown values. As shown in FIG. 4, the general form of suchestimation routine 130 can include first determining the number ofunknown parameters, which may include the trailer length D, the drawbarlength L, and the hitch angle γ or the hitch angle offset γ_(o), forexample, in step 134. Controller 28 then, in step 136 receives variousdata from certain ones of the vehicle sensors (e.g., vehicle speedsensor 58, vehicle yaw rate sensor 60, and trailer yaw rate sensor 25)as needed to identify a desired condition for calculating the unknownvalues in step 138. As discussed further below, certain specificcalculations are carried out using data obtained during steady-state(i.e. constant hitch angle and vehicle speed) movement of vehicle 14towing trailer 12, at a particular range of hitch angle γ, or the like.

Upon detecting a correct condition for continuing estimation routine130, controller 28, in step 140, can receive a particular set ofmeasurements relating to various dynamic parameters of the kinematicmodel. Such parameters can include steering angle δ, hitch angle γ,vehicle yaw rate ω1 and trailer yaw rate ω2, for example, depending onthe particular embodiment of routine 130 used and the available andunknown measurements. Regardless of the particular measurementsobtained, each such measurement is taken at the same instance in timesuch that each measurement corresponds to a set of measurements from thesame time. The measurements are received by controller 28 and stored,for example in memory 86, and are associated with each other accordingto the time with which they are associated. In this manner, a particularnumber of measurement sets can be taken to correspond with the number ofunknown parameters in step 142 such that a number of equations based onthe kinematic model can be derived to correspond to the number ofunknowns in step 144. In this manner, a number of equations equal to thenumber of unknowns can be obtained such that controller 28, in step 146,can solve for the unknowns to obtain estimates therefor. The result is acomplete kinematic model, where static values, such as drawbar length Land trailer length D can be stored in memory, and where dynamic values,such as γ can be calculated continuously using a simplified model suchthat controller 28 can use such values in a subsequent implementation ofcurvature routine 98. Controller 28 can solve the obtained equations forthe unknown values using one or more known processes or algorithms forsolving sets of equations for unknown variables, which may be includedwithin the programming of controller 28 or otherwise embedded within thelogic structure thereof. It is further noted that, as curvature routine98 requires values for trailer length D and drawbar length L to bestored in memory 186, system 10 may require that vehicle 14 be drivenwithout use of curvature routine 98 until such time that controller 28has been able to execute estimation routine 130 to obtain acceptableestimates for such values.

As shown in FIG. 5, one particular implementation of the estimationroutine 130 can be used to determine the hitch angle offset γ_(o) andthe trailer length D under two steady-state conditions for the hitchangle γ and the steering angle δ. In particular, using the kinematicmodel described above, the instantaneous hitch angle velocity {dot over(γ)} can be:

$\overset{.}{\gamma} = {\frac{d\;\gamma}{dt} = {{\frac{v}{D}\sin\;\gamma} + {\left( {1 + {\frac{L}{D}\cos\;\gamma}} \right)\frac{v}{W}\tan\;{\delta.}}}}$In step 136 a, controller 28 looks for conditions that indicate asteady-state for the hitch angle γ and for the steering angle δ, bywhich both the hitch angle velocity {dot over (γ)} is determined to bezero for a predetermined interval and the steering angle δ is maintainedconstant. Under such conditions, it is, therefore, known that in theabove equation {dot over (γ)}=0. Further, in step 138 b controller 28can look for a steady state condition with a low hitch angle γ, such asless than 10° (0.2 rad), which allows cos γ to be approximated as 1 andsin γ to be approximated as γ. By initially assuming these conditions tobe true, and simplifying, it is determined that:

${\tan\;\delta} = {\frac{{- W}\;\gamma}{L + D}.}$Since the routine 130 in the present example is looking to determine thehitch angle offset, γ_(o), the hitch angle γ in the above equation canbe substituted with γ_(m)-γ_(o), which can be solved for γ_(m) as afunction of tan δ to arrive at:

$\gamma_{m} = {\gamma_{o} - {\left( \frac{L + D}{W} \right)\tan\;{\delta.}}}$By collecting and storing two separate steady-state, low-angle valuesfor the hitch angle γ (steps 138 a, 138 b, 140, and 142), the kinematicmodel can be used to determine the unknown values in step 140. Inparticular, in step 148 the measured values can be considered datapoints in the above linear equation, wherein the hitch angle bias γ_(o)is the Y-intercept and (L+W)/D is the slope. It is noted that suchvalues should be taken such that the difference in the measurements isgreater than any known errors or system noise. With the two data pointsets, discussed above, noted as γ_(m1), γ_(m2), δ₁, and δ₂, theabove-equation can be re-written and solved for an estimate of (L+W)/Daccording to the following equation:

$\left( \frac{L + W}{D} \right) \approx {{\frac{\gamma_{m\; 1} - \gamma_{m\; 2}}{\delta_{1} - \delta_{2}}}.}$

Accordingly, when the drawbar length L and the wheelbase W are known,the stored values for the measured hitch angle γ_(m) and the steeringangle δ can be used to determine an estimate of the trailer length Dthat can be stored in memory 186 (step 150). Again, using the kinematicmodel, an equation is derived for the hitch angle offset γ_(o):

$\gamma_{o} = {{\gamma_{m\; 1} + {\left( \frac{L + D}{W} \right)\tan\;\delta_{1}}} = {\gamma_{m\; 2} + {\left( \frac{L + D}{W} \right)\tan\;{\delta_{2}.}}}}$Using this equation, the hitch angle offset γ_(o) can be calculated instep 152 using the measured values for hitch angle γ_(m) and thesteering angle δ, the known values for drawbar length L and wheelbase W,as well as the estimated trailer length D obtained in step 148. Thisvalue can be stored in memory 186 in step 154. In the alternative, thehitch angle offset γ_(o) can be obtained by continuing to accumulatedata points for the measured hitch angle γ_(m) and the steering angle δand averaging a sum of the above equations over time.

In a variation of such a routine 130, as depicted in FIG. 6, controller28 can look for dynamic, low hitch angle γ conditions in steps 136, 138a, and 138 b. Such a routine 130 can then take three measurements foreach of hitch angle γ_(m), the steering angle δ, the hitch angle rate{dot over (γ)}, and the vehicle speed ν. The measurement for hitch anglerate {dot over (γ)} can be obtained by tracking the hitch angle γ over apredetermined time interval, which may be less than one second. Thehitch angle γ_(m) measurement can be an average of the hitch anglethroughout the time interval used to measure the hitch angle rate {dotover (γ)}. Alternatively, the measured hitch angle γ_(m) can correspondto the hitch angle at the beginning, end, or a mid-point of themeasurement used to determine the hitch angle rate {dot over (γ)},assuming that for such low-angle conditions, any hitch angleacceleration will not negatively affect the hitch angle rate {dot over(γ)} measurement. Once three sets of contemporaneous measurements havebeen received (steps 140 and 142), a further equation derived from thekinematic model that includes the dynamic conditions of hitch angle rate{dot over (γ)} and vehicle speed ν can be used to solve for the hitchangle offset, the trailer length D, and the drawbar length L. Inparticular, the equation is:

$\gamma_{m} = {\gamma_{o} - {\left( \frac{L + D}{W} \right)\tan\;\delta} + {D{\frac{\overset{.}{\gamma}}{v}.}}}$This equation can be solved for all three unknowns simultaneously, orcan be solved for D and L first, with the hitch angle offset γ_(o) as avariable. The hitch angle offset γ_(o) can then be determined by anaverage of the sum of a dynamic kinematic model equation over a periodof time according to the equation:

$\gamma_{o} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{\left\lbrack {\left( \gamma_{m} \right)_{i} + {\left( \frac{L + D}{W} \right)\left( {\tan\;\delta} \right)_{i}} - {D\left( \frac{\overset{.}{\gamma}}{v} \right)}} \right\rbrack.}}}$In instances wherein the hitch angle offset γ_(o) is determined as anaverage over time, the trailer length D and the drawbar length L canfirst be determined using two of the sets of contemporaneousmeasurements discussed above, with the hitch angle offset γ_(o) beingseparately determined by the third set of measurements beingsubsequently taken over time. Further, in instances where the drawbarlength L is known, two sets of contemporaneous measurements can be usedto solve for trailer length D and hitch angle offset γ_(o).

Turning now to FIG. 7, a further variation of estimation routine 130 isdepicted in which the trailer length D, the drawbar length L, and thehitch angle offset γ_(o), as needed using the vehicle yaw rate, thetrailer yaw rate, the measured hitch angle γ_(m) and the steering anglerate dδ/dt (or {dot over (δ)}). The basis for the equation used for theestimates using these measurements is:

$\frac{d\;\gamma}{d\;\delta} = {\frac{\left( {D + {L\;\cos\;\gamma}} \right)\left( {\sec\;\delta} \right)^{2}}{{W\;\cos\;\gamma} + {L\;\sin\;{\gamma tan\delta}}}.}$Given that, in certain conditions, including low-angle conditions, tan δand sin γ can be approximated as zero and that sec δ and cos γ can beapproximated as 1, the equation can be approximated in a simplified formas:

$\frac{d\;\gamma}{d\;\delta} = {\frac{\frac{d\;\gamma}{dt}}{\frac{d\;\delta}{dt}} \approx \frac{\left( {D + {L\;\cos\;\gamma}} \right)}{W} \approx {\left( \frac{D + L}{W} \right).}}$It is further known that the hitch angle rate dγ/dt (or {dot over (γ)})can be determined as the difference between the trailer yaw rate ω₂ andthe vehicle yaw rate ω₁, the equation can be rewritten in terms of thetrailer yaw rate ω2, the vehicle yaw rate ω1, and the hitch angle γ as:

${\omega_{2} - \omega_{1}} \approx {\frac{d\;\delta}{dt}{\frac{\left( {D + {L\;\cos\;\gamma}} \right)}{W}.}}$This equation can be solved for D, with inputs for the trailer yaw rateω₂, the vehicle yaw rate and the measured hitch angle γ_(m) (step 146a), if, for example, the offset is known (step 156) or negligible.Because the hitch angle γ is equal to the sum of the measured hitchangle γ_(m) and the hitch angle offset γ_(o), the equation can be solvedincluding for the hitch angle offset γ_(o) using the measured hitchangle γ_(m) (step 158). As discussed above, if the drawbar length L, forexample, is known, then two sets of contemporaneous measurements for thevehicle yaw rate, the trailer yaw rate, the measured hitch angle γ_(m)and the steering angle rate dδ/dt can be used (step 160) instead ofthree.

In another embodiment, an estimation routine 230 is shown in FIG. 8, inwhich the trailer length D can be calculated by measuring the hitchangle γ and the steering angle δ over a period of time (step 236) andusing the collected measurements to estimate dγ/dδ, which can be used tosolve for the trailer length D. In such an instance the number ofmeasurements is inherently greater than the number of unknowns to besolved for, but can still be considered to correspond to the number ofunknowns in that a certain number of measurements are desired based onthe method of determining the unknown value. In the present instance,the controller 28 takes the data collected for the hitch angle γ and thesteering angle δ and fits a linear curve to such data (step 238), asshown in FIGS. 9 and 10, for example, to estimate dγ/dδ by the slope ofthe line. As such, in one example, measurements may be taken for apredetermined number of instances or may be taken with a curveconstantly fit to the collected data until a desired correlationcoefficient is reached or until such a line appears to converge to aconstant result.

As shown in FIG. 8, the estimation routine 230 can begin by receivingmeasurements for the steering angle δ and the hitch angle γ for aninterval (step 236), which may be as described above. In step 238,controller 28 fits a curve to the accumulated data, an example of whichis shown in FIG. 8, in which the hitch angle γ is plotted on the Y-axisagainst the steering angle γ on the X-axis, resulting in the data plot262 depicted. The curve 268 determined by controller 28 to best fit thedata is further illustrated. In one example, the kinematic model is usedto derive the equation:

$D \approx {W{\frac{d\;\gamma}{d\;\delta}.}}$This equation can be used to approximately solve for trailer length D,given the known wheelbase W. In another aspect, a more accurate resultmay be obtained using the equation:

$D = {{W\frac{d\;\gamma}{d\;\delta}} - {L\;\cos\;{\gamma.}}}$Again, this equation can be used to determine the trailer length D,given known values for the drawbar length L and the wheelbase W (step242), the determined trailer length D being subsequently stored inmemory (step 244). In general, the measurement used for hitch angle γcan be the highest value therefor in the recorded data set. In a furtherexample, a still more accurate result can be obtained by the equation:

$\frac{d\;\gamma}{d\;\delta} = {\frac{\left( {D + {L\;\cos\;\gamma}} \right)\left( {\sec\;\delta} \right)^{2}}{{W\;\cos\;\gamma} + {L\;\sin\;{\gamma tan\delta}}}.}$In this equation, the selected value for hitch angle γ can be thehighest measured hitch angle in the data set and the steering angle δused can be the value thereof corresponding to the selected hitch angleγ (step 240). In the example depicted in FIG. 8, the wheelbase D ofvehicle 14 is about 4 meters and the drawbar length L is about 1.39meters. The slope of the curve fit in the example of FIG. 8 is about0.87. Using the highest value for the hitch angle, which is 0.2 radians,and the corresponding steering angle of 0.1 radians, the trailer lengthD can be approximated as 2.04 meters or about 2 meters. As depicted inFIG. 9, an increasing trailer length is shown as resulting in anincreased value for dγ/dδ. In particular, the line 264 a based on data262 a corresponding to the shortest trailer length D of 2 meters has thelowest slope. Lines 264 b, 264 c, and 264 d based on data 262 a, 262 b,262 c, and 262 d corresponding increasing trailer lengths D of 2.5,2.75, and 3 meters have correspondingly increasing slopes.

An embodiment of the curvature routine 98 of the trailer backup assistsystem 10 is illustrated in FIG. 12, showing the general architecturallayout whereby a measurement module 88, a hitch angle regulator 90, anda curvature regulator 92 are routines that may be stored in the memory86 of the controller 28. In the illustrated layout, the steering inputdevice 18 provides a desired curvature κ₂ value to the curvatureregulator 92 of the controller 28, which may be determined from thedesired backing path 26 that is input with the steering input device 18.The curvature regulator 92 computes a desired hitch angle γ(d) based onthe current desired curvature κ₂ along with the steering angle δprovided by a measurement module 88 in this embodiment of the controller28. The measurement module 88 may be a memory device separate from orintegrated with the controller 28 that stores data from sensors of thetrailer backup assist system 10, trailer sensor module 20, the vehiclespeed sensor 58, the steering angle sensor, or alternatively themeasurement module 88 may otherwise directly transmit data from thesensors without functioning as a memory device. Once the desired hitchangle γ(d) is computed by the curvature regulator 92 the hitch angleregulator 90 generates a steering angle command based on the computeddesired hitch angle γ(d) as well as the measured hitch angle γ_(m) or anotherwise estimated hitch angle γ and a current velocity ν of thevehicle 14. The steering angle command is supplied to the power assiststeering system 62 of the vehicle 14, which is then fed back to themeasurement module 88 to reassess the impacts of other vehiclecharacteristics impacted from the implementation of the steering anglecommand or other changes to the system. Accordingly, the curvatureregulator 92 and the hitch angle regulator 90 continually processinformation from the measurement module 88 to provide accurate steeringangle commands that place the trailer 12 on the desired curvature κ₂ andthe desired backing path 26, without substantial overshoot or continuousoscillation of the path of travel about the desired curvature κ₂.

As also shown in FIG. 13, the embodiment of the curvature routine 98shown in FIG. 12 is illustrated in a control system block diagram.Specifically, entering the control system is an input, κ₂, whichrepresents the desired curvature 26 of the trailer 12 that is providedto the curvature regulator 92. The curvature regulator 92 can beexpressed as a static map, p(κ₂, δ), which in one embodiment is thefollowing equation:

${p\left( {\kappa_{2},\delta} \right)} = {\tan^{- 1}\left( \frac{{\kappa_{2}D} + {L\;{\tan(\delta)}}}{{\kappa_{2}{DL}\;{\tan(\delta)}} - W} \right)}$

Where,

κ₂ represents the desired curvature of the trailer 12 or 1/r₂ as shownin FIG. 3;

δ represents the steering angle;

L represents the distance from the rear axle of the vehicle 14 to thehitch pivot point;

D represents the distance from the hitch pivot point to the axle of thetrailer 12; and

W represents the distance from the rear axle to the front axle of thevehicle 14.

With further reference to FIG. 13, the output hitch angle of p(κ₂, δ) isprovided as the reference signal, γ_(ref), for the remainder of thecontrol system, although the steering angle δ value used by thecurvature regulator 92 is feedback from the non-linear function of thehitch angle regulator 90. It is shown that the hitch angle regulator 90uses feedback linearization for defining a feedback control law, asfollows:

${g\left( {u,\gamma,v} \right)} = {\delta = {{\tan^{- 1}\left( {\frac{W}{v\left( {1 + {\frac{L}{D}{\cos(\gamma)}}} \right)}\left( {u - {\frac{v}{D}{\sin(\gamma)}}} \right)} \right)}.}}$

As also shown in FIG. 12, the feedback control law, g(u, γ, ν), isimplemented with a proportional integral (PI) controller, whereby theintegral portion substantially eliminates steady-state tracking error.More specifically, the control system illustrated in FIG. 12 may beexpressed as the following differential-algebraic equations:

${\overset{.}{\gamma}(t)} = {{\frac{v(t)}{D}{\sin\left( {\gamma(t)} \right)}} + {\left( {1 + {\frac{L}{D}{\cos\left( {\gamma(t)} \right)}}} \right)\frac{v(t)}{W}\overset{\_}{\delta}\mspace{14mu}{and}}}$${\tan(\delta)} = {\overset{\_}{\delta} = {\frac{W}{{v(t)}\left( {1 + {\frac{L}{D}{\cos\left( {\gamma(t)} \right)}}} \right)}{\left( {{K_{P}\left( {{p\left( {\kappa_{2},\delta} \right)} - {\gamma(t)}} \right)} - {\frac{v(t)}{D}{\sin\left( {\gamma(t)} \right)}}} \right).}}}$

It is contemplated that the PI controller may have gain terms based ontrailer length D since shorter trailers will generally have fasterdynamics. In addition, the hitch angle regulator 90 may be configured toprevent the desired hitch angle γ(d) to reach or exceed a jackknifeangle γ(j), as computed by the controller or otherwise determined by thetrailer backup assist system 10, as disclosed in greater detail herein.

Referring now to FIG. 13, in the illustrated embodiments of thedisclosed subject matter, it is desirable to limit the potential for thevehicle 14 and the trailer 12 to attain a jackknife angle (i.e., thevehicle/trailer system achieving a jackknife condition). A jackknifeangle γ(j) refers to a hitch angle γ that while backing cannot beovercome by the maximum steering input for a vehicle such as, forexample, the steered front wheels of the vehicle 14 being moved to amaximum steered angle δ at a maximum rate of steering angle change. Thejackknife angle γ(j) is a function of a maximum wheel angle for thesteered wheels of the vehicle 14, the wheel base W of the vehicle 14,the distance L between hitch point and the rear axle of the vehicle 14,and the trailer length D between the hitch point and the axle of thetrailer 12 or the effective axle when the trailer 12 has multiple axles.When the hitch angle γ for the vehicle 14 and the trailer 12 achieves orexceeds the jackknife angle γ(j), the vehicle 14 may be pulled forwardto reduce the hitch angle γ. Thus, for limiting the potential for avehicle/trailer system attaining a jackknife angle, it is preferable tocontrol the yaw angle of the trailer 12 while keeping the hitch angle γof the vehicle/trailer system relatively small.

A kinematic model representation of the vehicle 14 and the trailer 12can also be used to determine a jackknife angle for the vehicle-trailercombination. Accordingly, with reference to FIG. 13, a steering anglelimit for the steered front wheels requires that the hitch angle γcannot exceed the jackknife angle γ(j), which is also referred to as acritical hitch angle γ. Thus, under the limitation that the hitch angleγ cannot exceed the jackknife angle γ(j), the jackknife angle γ(j) isthe hitch angle γ that maintains a circular motion for thevehicle/trailer system when the steered wheels 64 are at a maximumsteering angle δ_((max)). The steering angle for circular motion withhitch angle γ is defined by the following equation.

${\tan\;\delta_{\max}} = {\frac{w\;\sin\;\gamma_{\max}}{D + {L\;\cos\;\gamma_{\max}}}.}$

Solving the above equation for hitch angle γ allows jackknife angle γ(j)to be determined. This solution, which is shown in the followingequation, can be used in implementing trailer backup assistfunctionality in accordance with the disclosed subject matter formonitoring hitch angle γ in relation to jackknife angle.

${\cos\;\overset{\_}{\gamma}} = \frac{{- b} \pm \sqrt{b^{2} - {4{ac}}}}{2a}$

where,

a=L² tan² δ(max)+W²;

b=2 LD tan² δ(max); and

c=D² tan² δ(max)−W².

In certain instances of backing the trailer 12, a jackknife enablingcondition can arise based on current operating parameters of the vehicle14 in combination with a corresponding hitch angle γ. This condition canbe indicated when one or more specified vehicle operating thresholds aremet while a particular hitch angle γ is present. For example, althoughthe particular hitch angle γ is not currently at the jackknife angle forthe vehicle 14 and attached trailer 12, certain vehicle operatingparameters can lead to a rapid (e.g., uncontrolled) transition of thehitch angle γ to the jackknife angle for a current commanded trailercurvature and/or can reduce an ability to steer the trailer 12 away fromthe jackknife angle. One reason for a jackknife enabling condition isthat trailer curvature control mechanisms (e.g., those in accordancewith the disclosed subject matter) generally calculate steering commandsat an instantaneous point in time during backing of a trailer 12.However, these calculations will typically not account for lag in thesteering control system of the vehicle 14 (e.g., lag in a steering EPAScontroller). Another reason for the jackknife enabling condition is thattrailer curvature control mechanisms generally exhibit reduced steeringsensitivity and/or effectiveness when the vehicle 14 is at relativelyhigh speeds and/or when undergoing relatively high acceleration.

Jackknife determining information may be received by the controller 28,according to one embodiment, to process and characterize a jackknifeenabling condition of the vehicle-trailer combination at a particularpoint in time (e.g., at the point in time when the jackknife determininginformation was sampled). Examples of the jackknife determininginformation include, but are not limited to, information characterizingan estimated hitch angle γ, information characterizing a vehicleaccelerator pedal transient state, information characterizing a speed ofthe vehicle 14, information characterizing longitudinal acceleration ofthe vehicle 14, information characterizing a brake torque being appliedby a brake system of the vehicle 14, information characterizing apowertrain torque being applied to driven wheels of the vehicle 14, andinformation characterizing the magnitude and rate of driver requestedtrailer curvature. In this regard, jackknife determining informationwould be continually monitored, such as by an electronic control unit(ECU) that carries out trailer backup assist (TBA) functionality. Afterreceiving the jackknife determining information, a routine may processthe jackknife determining information for determining if thevehicle-trailer combination attained the jackknife enabling condition atthe particular point in time. The objective of the operation forassessing the jackknife determining information is determining if ajackknife enabling condition has been attained at the point in timedefined by the jackknife determining information. If it is determinedthat a jackknife enabling condition is present at the particular pointin time, a routine may also determine an applicable countermeasure orcountermeasures to implement. Accordingly, in some embodiments, anapplicable countermeasure will be selected dependent upon a parameteridentified as being a key influencer of the jackknife enablingcondition. However, in other embodiments, an applicable countermeasurewill be selected as being most able to readily alleviate the jackknifeenabling condition. In still another embodiment, a predefinedcountermeasure or predefined set of countermeasures may be theapplicable countermeasure(s).

As previously disclosed with reference to the illustrated embodiments,during operation of the trailer backup assist system 10, a driver of thevehicle 14 may be limited in the manner in which steering inputs may bemade with the steering wheel 68 of the vehicle 14 due to the powerassist steering system 62 being directly coupled to the steering wheel68. Accordingly, the steering input device 18 of the trailer backupassist system 10 may be used for inputting a desired curvature 26 of thetrailer 12, thereby decoupling such commands from being made at thesteering wheel 68 of the vehicle 14. However, additional embodiments ofthe trailer backup assist system 10 may have the capability toselectively decouple the steering wheel 68 from movement of steerablewheels of the vehicle 14, thereby allowing the steering wheel 68 to beused for commanding changes in the desired curvature 26 of a trailer 12or otherwise selecting a desired backing path during such trailer backupassist.

Referring now to FIG. 14, one embodiment of the steering input device 18is illustrated disposed on a center console 108 of the vehicle 14proximate a shifter 110. In this embodiment, the steering input device18 includes a rotatable knob 30 for providing the controller 28 with thedesired backing path of the trailer 12. More specifically, the angularposition of the rotatable knob 30 may correlate with a desiredcurvature, such that rotation of the knob to a different angularposition provides a different desired curvature with an incrementalchange based on the amount of rotation and, in some embodiments, anormalized rate, as described in greater detail herein.

The rotatable knob 30, as illustrated in FIGS. 14 and 15, may be biased(e.g., by a spring return) to a center or at-rest position P(AR) betweenopposing rotational ranges of motion R(R), R(L). In the illustratedembodiment, a first one of the opposing rotational ranges of motion R(R)is substantially equal to a second one of the opposing rotational rangesof motion R(L), R(R). To provide a tactile indication of an amount ofrotation of the rotatable knob 30, a force that biases the knob towardthe at-rest position P(AR) can increase (e.g., non-linearly) as afunction of the amount of rotation of the rotatable knob 30 with respectto the at-rest position P(AR). Additionally, the rotatable knob 30 canbe configured with position indicating detents such that the driver canpositively feel the at-rest position P(AR) and feel the ends of theopposing rotational ranges of motion R(L), R(R) approaching (e.g., softend stops). The rotatable knob 30 may generate a desired curvature valueas a function of an amount of rotation of the rotatable knob 30 withrespect to the at-rest position P(AR) and a direction of movement of therotatable knob 30 with respect to the at-rest position P(AR). It is alsocontemplated that the rate of rotation of the rotatable knob 30 may alsobe used to determine the desired curvature output to the controller 28.The at-rest position P(AR) of the knob corresponds to a signalindicating that the vehicle 14 should be steered such that the trailer12 is backed along a substantially straight backing path 114 (zerotrailer curvature request from the driver), as defined by thelongitudinal direction 22 of the trailer 12 when the knob was returnedto the at-rest position P(AR). A maximum clockwise and anti-clockwiseposition of the knob (i.e., limits of the opposing rotational ranges ofmotion R(R), R(L)) may each correspond to a respective signal indicatinga tightest radius of curvature (i.e., most acute trajectory or smallestradius of curvature) of a path of travel of the trailer 12 that ispossible without the corresponding vehicle steering information causinga jackknife condition.

As shown in FIG. 15, a driver can turn the rotatable knob 30 to providea desired curvature 26 while the driver of the vehicle 14 backs thetrailer 12. In the illustrated embodiment, the rotatable knob 30 rotatesabout a central axis between a center or middle position 114corresponding to a substantially straight backing path 26 of travel, asdefined by the longitudinal direction 22 of the trailer 12, and variousrotated positions 116, 118, 120, 122 on opposing sides of the middleposition 114, commanding a desired curvature 26 corresponding to aradius of the desired backing path of travel for the trailer 12 at thecommanded rotated position. It is contemplated that the rotatable knob30 may be configured in accordance with embodiments of the disclosedsubject matter and omit a means for being biased to an at-rest positionP(AR) between opposing rotational ranges of motion. Lack of such biasingmay allow a current rotational position of the rotatable knob 30 to bemaintained until the rotational control input device is manually movedto a different position. It is also conceivable that the steering inputdevice 18 may include a non-rotational control device that may beconfigured to selectively provide a desired curvature 26 and to overrideor supplement an existing curvature value. Examples of such anon-rotational control input device include, but are not limited to, aplurality of depressible buttons (e.g., curve left, curve right, andtravel straight), a touch screen on which a driver traces or otherwiseinputs a curvature for path of travel commands, a button that istranslatable along an axis for allowing a driver to input backing pathcommands, or a joystick type input and the like.

Referring to FIG. 16, an example of using the steering input device 18for dictating a curvature of a desired backing path of travel (POT) ofthe trailer 12 while backing up the trailer 12 with the vehicle 14 isshown. In preparation of backing the trailer 12, the driver of thevehicle 14 may drive the vehicle 14 forward along a pull-thru path (PTP)to position the vehicle 14 and trailer 12 at a first backup position B1.In the first backup position B1, the vehicle 14 and trailer 12 arelongitudinally aligned with each other such that a longitudinalcenterline axis L1 of the vehicle 14 is aligned with (e.g., parallelwith or coincidental with) a longitudinal centerline axis L2 of thetrailer 12. It is disclosed herein that such alignment of thelongitudinal axis L1, L2 at the onset of an instance of trailer backupfunctionality is not a requirement for operability of a trailer backupassist system 10, but may be done for calibration.

After activating the trailer backup assist system 10 (e.g., before,after, or during the pull-thru sequence), the driver begins to back thetrailer 12 by reversing the vehicle 14 from the first backup positionB1. So long as the rotatable knob 30 of the trailer backup steeringinput device 18 remains in the at-rest position P(AR) and no othersteering input devices 18 are activated, the trailer backup assistsystem 10 will steer the vehicle 14 as necessary for causing the trailer12 to be backed along a substantially straight path of travel, asdefined by the longitudinal direction 22 of the trailer 12, specificallythe centerline axis L2 of the trailer 12, at the time when backing ofthe trailer 12 began. When the trailer 12 reaches the second backupposition B2, the driver rotates the rotatable knob 30 to command thetrailer 12 to be steered to the right (i.e., a knob position R(R)clockwise rotation). Accordingly, the trailer backup assist system 10will steer the vehicle 14 for causing the trailer 12 to be steered tothe right as a function of an amount of rotation of the rotatable knob30 with respect to the at-rest position P(AR), a rate movement of theknob, and/or a direction of movement of the knob 30 with respect to theat-rest position P(AR). Similarly, the trailer 12 can be commanded tosteer to the left by rotating the rotatable knob 30 to the left. Whenthe trailer 12 reaches backup position B3, the driver allows therotatable knob 30 to return to the at-rest position P(AR) therebycausing the trailer backup assist system 10 to steer the vehicle 14 asnecessary for causing the trailer 12 to be backed along a substantiallystraight path of travel as defined by the longitudinal centerline axisL2 of the trailer 12 at the time when the rotatable knob 30 was returnedto the at-rest position P(AR). Thereafter, the trailer backup assistsystem 10 steers the vehicle 14 as necessary for causing the trailer 12to be backed along this substantially straight path to the fourth backupposition B4. In this regard, arcuate portions of a path of travel POT ofthe trailer 12 are dictated by rotation of the rotatable knob 30 andstraight portions of the path of travel POT are dictated by anorientation of the centerline longitudinal axis L2 of the trailer 12when the knob is in/returned to the at-rest position P(AR).

In the embodiment illustrated in FIG. 16, in order to activate thetrailer backup assist system 10, the driver interacts with the trailerbackup assist system 10 and automatically steers as the driver reversesthe vehicle 14. As discussed above, the driver may command the trailerbacking path by using a steering input device 18 and the controller 28may determine the vehicle steering angle to achieve the desiredcurvature 26, whereby the driver controls the throttle and brake whilethe trailer backup assist system 10 controls the steering.

With reference to FIG. 17, a method of operating one embodiment of thetrailer backup assist system 10 is illustrated, shown as one embodimentof the operating routine 132 (FIG. 2). In one aspect, system 10 can beconfigured to lock out or deactivate operating routine 132 untilestimates at least one of a trailer length D, draw bar length L, hitchangle offset γ_(o), or the like has been obtained in step 131 (discussedfurther above with reference to FIG. 4). After the required parametershave been estimated or otherwise determined, operating routine 132 isallowed to be initiated, as requested by a user, in step 134 (FIG. 17),as discussed above, using the trailer length D, drawbar length L, and/orhitch angle offset γ_(o) in the kinematic model and the variousequations used in operating routine 132 derived therefrom.

At step 134, the method is initiated by the trailer backup assist system10 being activated. It is contemplated that this may be done in avariety of ways, such by making a selection on the display 82 of thevehicle HMI 80. The next step 136, then determines the kinematicrelationship between the attached trailer 12 and the vehicle 14. Todetermine the kinematic relationship, various parameters of the vehicle14 and the trailer 12 must be sensed, input by the driver, or otherwisedetermined for the trailer backup assist system 10 to generate steeringcommands to the power assist steering system 62 in accordance with thedesired curvature or backing path 26 of the trailer 12, as discussedabove with reference to FIGS. 1-3

In one aspect, after the kinematic relationship is determined, thetrailer backup assist system 10 may proceed at step 160 to determine thecurrent hitch angle, which can be done using a hitch angle sensor 44, asdescribed above or by various calculations or estimations based on thekinematic model. Operating routine 132 continues at step 162 in whichthe position and rate of change is received from the steering inputdevice 18, such as the angular position and rate of rotation of therotatable knob 30, for determining the desired curvature 26. At step164, steering commands may be generated based on the desired curvature,correlating with the position and rate of change of the steering inputdevice 18. The steering commands and actuation commands generated may begenerated in conjunction with processing of the curvature routine 98, asprevious discussed. At step 166, the steering commands and actuationcommands have been executed to guide the trailer 12 on the desiredcurvature provided by the steering input device 18.

It will be understood by one having ordinary skill in the art thatconstruction of the described invention and other components is notlimited to any specific material. Other exemplary embodiments of theinvention disclosed herein may be formed from a wide variety ofmaterials, unless described otherwise herein.

For purposes of this disclosure, the term “coupled” (in all of itsforms, couple, coupling, coupled, etc.) generally means the joining oftwo components (electrical or mechanical) directly or indirectly to oneanother. Such joining may be stationary in nature or movable in nature.Such joining may be achieved with the two components (electrical ormechanical) and any additional intermediate members being integrallyformed as a single unitary body with one another or with the twocomponents. Such joining may be permanent in nature or may be removableor releasable in nature unless otherwise stated.

It is also important to note that the construction and arrangement ofthe elements of the invention as shown in the exemplary embodiments isillustrative only. Although only a few embodiments of the presentinnovations have been described in detail in this disclosure, thoseskilled in the art who review this disclosure will readily appreciatethat many modifications are possible (e.g., variations in sizes,dimensions, structures, shapes and proportions of the various elements,values of parameters, mounting arrangements, use of materials, colors,orientations, etc.) without materially departing from the novelteachings and advantages of the subject matter recited. For example,elements shown as integrally formed may be constructed of multiple partsor elements shown as multiple parts may be integrally formed, theoperation of the interfaces may be reversed or otherwise varied, thelength or width of the structures and/or members or connector or otherelements of the system may be varied, the nature or number of adjustmentpositions provided between the elements may be varied. It should benoted that the elements and/or assemblies of the system may beconstructed from any of a wide variety of materials that providesufficient strength or durability, in any of a wide variety of colors,textures, and combinations. Accordingly, all such modifications areintended to be included within the scope of the present innovations.Other substitutions, modifications, changes, and omissions may be madein the design, operating conditions, and arrangement of the desired andother exemplary embodiments without departing from the spirit of thepresent innovations.

It will be understood that any described processes or steps withindescribed processes may be combined with other disclosed processes orsteps to form structures within the scope of the present invention. Theexemplary structures and processes disclosed herein are for illustrativepurposes and are not to be construed as limiting.

It is also to be understood that variations and modifications can bemade on the aforementioned structures and methods without departing fromthe concepts of the present invention, and further it is to beunderstood that such concepts are intended to be covered by thefollowing claims unless these claims by their language expressly stateotherwise.

What is claimed is:
 1. A backup assist system for a vehicle and trailercombination, comprising: a steering system; a first sensor detecting afirst dynamic condition of the combination; and a controller: receivinga value for the first dynamic condition from the first sensor at aplurality of instances; solving for a corresponding plurality ofparameters in a kinematic model of the combination; and controlling thesteering system using the plurality of parameters in the kinematicmodel.
 2. The backup assist system of claim 1, wherein: the first sensoris a hitch angle sensor; the first dynamic condition is a hitch anglebetween the vehicle and the trailer; the system further includes asecond sensor comprising a steering angle sensor determining a steeringangle of the steering system; and the controller further receives aplurality of values for the steering angle for each of the plurality ofinstances.
 3. The backup assist system of claim 2, wherein: theplurality of instances includes two instances; and the plurality ofparameters solved for include a trailer length and a hitch angle bias.4. The backup assist system of claim 3, wherein the two instancesindicate a steady state condition of the combination.
 5. The backupassist system of claim 3, wherein the two instances each include a hitchangle of less than 10°.
 6. The backup assist system of claim 2, wherein:the plurality of instances includes three instances; and the pluralityof parameters solved for include a trailer length, a drawbar length, anda hitch angle bias.
 7. The backup assist system of claim 2, wherein: thecontroller uses the values received for the hitch angle and the steeringangle to fit a linear curve to the hitch angle values against thesteering angle values, the linear curve correlating with a rate ofchange of the steering angle over a rate of change of the hitch angle;and the controller solves for a trailer length using the rate of changeof the steering angle over a rate of change of the hitch angle in thekinematic model.
 8. The backup assist system of claim 1, wherein: thefirst sensor is a yaw rate sensor of the trailer; the first dynamiccondition is a yaw rate of the trailer; the system further includes asecond sensor comprising a vehicle yaw rate sensor determining a yawrate of the vehicle; and the controller further receives a plurality ofvalues for the vehicle yaw rate for each of the plurality of instances.9. The backup assist system of claim 8, wherein: the plurality ofinstances includes two instances; and the plurality of parameters solvedfor include a trailer length and a hitch angle bias.
 10. The backupassist system of claim 1, wherein controlling the steering system usingthe plurality of parameters in the kinematic model includes determininga steering angle according to a curvature command.
 11. A vehicle,comprising: a steering system; a first sensor detecting a first dynamiccondition of at least one of the vehicle and the vehicle in acombination with a trailer; and a trailer backup assist system,comprising a controller: receiving a value for the first dynamiccondition from the first sensor in at least one instance; solving for atleast one parameter corresponding in number to the at least one instancein a kinematic model of the combination; and controlling the steeringsystem using the at least one parameter in the kinematic model.
 12. Thevehicle of claim 11, further including a second sensor comprising asteering angle sensor determining a steering angle of the steeringsystem, wherein: the first sensor is a hitch angle sensor; the firstdynamic condition is a hitch angle between the vehicle and the trailer;and the controller of the trailer backup assist system further receivesat least one value for the steering angle for each of the at least oneinstance.
 13. The vehicle of claim 12, wherein: the at least oneinstance includes two instances; and the at least one parameter solvedfor includes a trailer length and a hitch angle bias.
 14. The vehicle ofclaim 12, wherein: the controller uses the values received for the hitchangle and the steering angle to fit a linear curve to the hitch anglevalues against the steering angle values, the linear curve correlatingwith a rate of change of the steering angle over a rate of change of thehitch angle; and the controller solves for a trailer length using therate of change of the steering angle over a rate of change of the hitchangle in the kinematic model.
 15. The vehicle of claim 11, wherein: thefirst sensor is a yaw rate sensor of the trailer; the first dynamiccondition is a yaw rate of the trailer; the vehicle further includes asecond sensor comprising a vehicle yaw rate sensor determining a yawrate of the vehicle; the controller further receives a plurality ofvalues for the vehicle yaw rate for each of the at least one instance;and the at least one parameter solved for includes a trailer length anda hitch angle.
 16. A method for assisting a vehicle in reversing atrailer, comprising: determining unknown values for a plurality ofparameters in a combination of the vehicle and the trailer, including:receiving a first measurement for a first dynamic condition of thecombination at a plurality of instances; and solving for the parametersin a kinematic model of the combination; and implementing a reversingoperation including controlling a vehicle steering system using theplurality of parameters.
 17. The method of claim 16, wherein: the firstdynamic condition is a hitch angle between the vehicle and the trailer;and determining the unknown values further includes receiving a secondmeasurement for a steering angle of the steering system at the pluralityof instances.
 18. The method of claim 17, wherein: the plurality ofinstances includes two instances; and the plurality of parameters solvedfor include a trailer length and a hitch angle bias.
 19. The method ofclaim 17, wherein solving for the parameters in the kinematic model ofthe combination includes: using the values received for the hitch angleand the steering angle to fit a linear curve to the hitch angle valuesagainst the steering angle values, the linear curve correlating with arate of change of the steering angle over a rate of change of the hitchangle; and solving for a trailer length using the rate of change of thesteering angle over a rate of change of the hitch angle in the kinematicmodel.
 20. The method of claim 16, wherein: the first dynamic conditionis a yaw rate of the trailer; determining the unknown values furtherincludes receiving a second measurement for a yaw rate of the vehiclefor each of the plurality of instances; and the plurality of parameterssolved for include a trailer length and a hitch angle.